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Physical Review A

Field cancellation by a two-level atom in a multimode cavity driven by a time-dependent field

David A. Cardimona, Karl W. Koch, Paul M. Alsing

Published Jan 1, 1997• 2 citations
Publisher

Abstract

We investigate the behavior of a two-level atom in a multimode cavity driven from the side by a time-dependent field. The time-dependent fields we have looked at are (i) pure amplitude modulated, (ii) pure frequency modulated, (iii) single sideband, and (iv) general three-mode fields. Each of these fields results in two (for the single-sideband case) or three modes separated by the modulation frequency. We find that when the driving field mode spacing is a multiple of the cavity mode spacing, the multimode cavity field created by the driven two-level atom becomes exactly 180\ifmmode^\circ\else\textdegree\fi{} out of phase with the external driving field in steady state. This results in a zero net field at the position of the atom and, hence, the atom remains unexcited regardless of the strength of the external driving field. This is very reminiscent of the field-induced transparency effect as described by Cardimona et al. [J. Phys. B 15, 55 (1982)] in which the various dipole transitions of a multilevel atom dressed by a coherent field are driven 180\ifmmode^\circ\else\textdegree\fi{} out of phase with each other, producing a zero net fluorescence. We also show that, in the limit of an infinite cavity, the multimode equations reduce to the neoclassical equations of Stroud and Jaynes [Phys. Rev. A 1, 106 (1970)].

DOI
10.1103/physreva.55.787

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Physical Review A•Aug 1, 1998•35 citations
We investigate the behavior of a two-level atom in a multimode cavity driven from the side by a time-dependent field. The time-dependent fields we have looked at are (i) pure amplitude modulated, (ii) pure frequency modulated, (iii) single sideband, and (iv) general three-mode fields. Each of these fields results in two (for the single-sideband case) or three modes separated by the modulation frequency. We find that when the driving field mode spacing is a multiple of the cavity mode spacing, the multimode cavity field created by the driven two-level atom becomes exactly 180\ifmmode^\circ\else\textdegree\fi{} out of phase with the external driving field in steady state. This results in a zero net field at the position of the atom and, hence, the atom remains unexcited regardless of the strength of the external driving field. This is very reminiscent of the field-induced transparency effect as described by Cardimona et al. [J. Phys. B 15, 55 (1982)] in which the various dipole transitions of a multilevel atom dressed by a coherent field are driven 180\ifmmode^\circ\else\textdegree\fi{} out of phase with each other, producing a zero net fluorescence. We also show that, in the limit of an infinite cavity, the multimode equations reduce to the neoclassical equations of Stroud and Jaynes [Phys. Rev. A 1, 106 (1970)].
We investigate quantum interference and classical-interference effects when three-level atoms in the ``$\ensuremath{\Lambda}$'' or ``V'' configuration interact with both a cavity-field mode and an external driving field mode. We describe electromagnetically induced transparency ($\ensuremath{\Lambda}$ configuration), as well as a ``field-induced transparency'' (V configuration), and we go beyond the weak cavity-field studies of previous papers by utilizing a Heisenberg-picture density matrix approach. We find that under certain circumstances the cavity field evolves to be equal in magnitude to, but $180\ifmmode^\circ\else\textdegree\fi{}$ out of phase with, the external pump field when the pump-field frequency equals the cavity frequency, a surprising effect found in two-level atoms in a cavity excited by an external pump field that persists in three-level atoms. The better the cavity, the quicker this buildup occurs. When the cavity field reaches this ``out-of-phase'' condition, the resonance fluorescence from the atom in the cavity goes to zero. This is a purely classical-interference effect between the two out-of-phase fields, with the resonance fluorescence going to zero at the same time as the two excited state populations go to zero. This is quite different from the quantum interference that occurs under the right circumstances when the state populations are coherently driven into a linear combination that is decoupled from any applied field and population is trapped in the excited states (``coherent population trapping''). When the cavity frequency is tuned to the frequency at which quantum interference would occur, the two interference effects compete with each other. The cavity field begins to evolve toward the $180\ifmmode^\circ\else\textdegree\fi{}$ out-of-phase condition, thereby approaching a classical destructive interference condition with the pump field. Then at some point before 100% classical interference occurs, depending on the cavity damping rate and atom/cavity coupling strength, the atom builds up its coherence between state populations to produce the quantum interference effect. At that point, the atom becomes transparent and resonance fluorescence disappears, including fluorescence into the cavity, thereby causing the cavity field to die away.
We investigate the fluorescence spectrum of a two-level atom driven by a multiple amplitude-modulated field. The driving field is modeled as a polychromatic field composed of a strong central (resonant) component and a large number of symmetrically detuned sideband fields displaced from the central component by integer multiples of a constant detuning. Spectra obtained here differ qualitatively from those observed for a single pair of modulating fields [B. Blind, P.R. Fontana, and P. Thomann, J. Phys. B 13, 2717 (1980)]. In the case of a small number of the modulating fields, a multipeaked spectrum is obtained with the spectral features located at fixed frequencies that are independent of the number of modulating fields and their Rabi frequencies. As the number of the modulating fields increases, the spectrum ultimately evolves to the well-known Mollow triplet with the sidebands shifted from the central component by an effective Rabi frequency whose magnitude depends on the initial relative phases of the components of the driving field. For equal relative phases, the effective Rabi frequency of the driving field can be reduced to zero resulting in the disappearance of fluorescence spectrum, i.e., the atom can stop interacting with the field. When the central component and the modulating fields are $180\ifmmode^\circ\else\textdegree\fi{}$ out of phase, the spectrum retains its triplet structure with the sidebands located at frequencies equal to the sum of the Rabi frequencies of the component of the driving field. Moreover, we show that the frequency of spontaneous emission can be controlled and switched from one frequency to another when the Rabi frequency or initial phase of the modulating fields are varied.
We analyze the time-dependent physical spectrum of a driven Jaynes-Cummings model in which both the two-level system and the quantized cavity mode are subject to coherent classical driving. The time-dependent Hamiltonian is mapped, via well-defined unitary transformations, onto an effective stationary Jaynes-Cummings form. Within this framework, we derive closed-form expressions for the two-time correlation functions of both the atomic and field operators. These correlation functions are subsequently used to evaluate the time-dependent physical spectrum according to the Eberly-Wódkiewicz definition, which properly accounts for finite spectral resolution and transient emission dynamics. We show that the external driving leads to substantial modifications of the atomic spectral response, including controllable frequency shifts and asymmetric line shapes. Importantly, we identify a regime in which the driving parameters are chosen such that the coherent displacement induced in the cavity field exactly cancels out the initial coherent amplitude. In this limit, the system dynamics reduce to that of an effectively vacuum-initialized Jaynes-Cummings model, and the standard vacuum Rabi splitting is recovered. This behavior provides a clear and physically transparent interpretation of the spectral features as arising from coherent field displacement rather than from modifications of the underlying atom-cavity coupling.
We show that a dynamical suppression of spontaneous emission, predicted for a three-level atom [S.-Y. Zhu and M. O. Scully, Phys. Rev. Lett. 76, 388 (1996)] can occur in a two-level atom driven by a polychromatic field. We find that the quantum interference, responsible for the cancellation of spontaneous emission, appears between different channels of transitions among the dressed states of the driven atom. We discuss the effect for bichromatic and trichromatic (amplitude-modulated) fields and find that these two cases lead to the cancellation of spontaneous emission in different parts of the fluorescence spectrum. Our system has the advantage of being easily accessible by current experiments.
We study the dynamics of a collection of two-level atoms interacting with a single mode of a quantized field in a dissipative cavity in the dispersive regime. The quantized mode is driven by a classical driving field. The steady-state density matrix is obtained. The influence of the driving field on the quantized driven field and on atomic properties in both the dissipative and the lossless cases is studied. The atomic decoherence time in the dissipative-driven case is obtained. We show that the external driving field strongly suppresses the atomic coherence (in comparison with the dissipative cavity without the driving field).
A cavity-modified master equation is derived for a coherently driven two-level atom coupled to a single-mode cavity in the bad cavity limit, in which the cavity frequency is tuned to either the center or one of the sidebands of the Mollow triplet. The atomic populations in both the bare- and dressed-state representations are analyzed in terms of the cavity-modified transition rates. In the bare-state basis, the role of the cavity may be interpreted as enhancing the stimulated absorption of the atom while suppressing the stimulated emission. The bare-state population may thus be inverted under appropriate conditions. The dressed-state inversion, however, originates from the enhancement of the atom-cavity interaction when the cavity is resonant with the atomic dressed-state transition. We show that two-phase quadratures of the atomic polarization decay at different rates. The decay of the in-phase (or out-of-phase) quadrature may be greatly inhibited as the driving intensity increases, depending on the cavity resonant frequency. The spectrum of the atomic fluorescence emitted out the side of the cavity is also studied. The spectral profiles are sensitive to the cavity frequency. When the cavity frequency is tuned to the center of the Mollow resonances, the fluorescence spectrum is symmetrical with three peaks whose linewidths and heights are intensity dependent. When the cavity frequency is tuned to one of the Mollow sidebands, however, it is asymmetric, and the central peak and the sideband on resonance with the cavity can be significantly suppressed for strong driving fields. All three spectral lines can be narrowed by increasing the Rabi frequency. The physics of these striking spectral features is explored in the dressed-state basis. We also investigate the probe absorption spectrum. When the cavity frequency is tuned to the center of the Mollow fluorescence triplet, the central component exhibits a Lorentzian line shape, while the side bands show the Rayleigh-wing line shape. Probe gain may occur at line center due to cavity-induced, bare-state population inversion. When the cavity is tuned to resonance with one sideband, only two sidebands, with Lorentzian profiles, dominate. Gain can occur at the sideband far off resonant with the cavity. The sideband gain is a consequence of an unbalanced dressed-state population distribution.